{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HVICV2JYPPSU3XPJXQSQFMKC23","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"661b8fd3103199048093d76f4acbbd7015b89ea9b9b5f9200e910682591bdc14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-09T13:39:23Z","title_canon_sha256":"0e951bdc7455cd120d94c358f052cc7a0c7e42710bf53dcdbf12c4af4be05c90"},"schema_version":"1.0","source":{"id":"1603.02884","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02884","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02884v4","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02884","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"HVICV2JYPPSU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HVICV2JYPPSU3XPJ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HVICV2JY","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:802f98693c9a8ae81c6290dd9058c2f44f5aafb9cd3cfd6a3c415cd8b00b3e10","target":"graph","created_at":"2026-05-18T00:24:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of fixed level when $n \\geq 2$. This is in contrast with the result of Kiming, Rustom and Wiese which establishes a uniform weight bound on strong eigenforms mod $p^n$. As a step towards studying weights bounds for weak eigenforms mod $p^n$, we provide a criterion which allows us to detect whether a given dc-weak eigenform mod $p^n$ is weak.","authors_text":"Nadim Rustom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-09T13:39:23Z","title":"Filtrations of dc-weak eigenforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02884","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:01a7894c7b5739d3ce8057b6e2f196e90b028ffeab67a9ecf155f5d1dba02fa0","target":"record","created_at":"2026-05-18T00:24:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"661b8fd3103199048093d76f4acbbd7015b89ea9b9b5f9200e910682591bdc14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-09T13:39:23Z","title_canon_sha256":"0e951bdc7455cd120d94c358f052cc7a0c7e42710bf53dcdbf12c4af4be05c90"},"schema_version":"1.0","source":{"id":"1603.02884","kind":"arxiv","version":4}},"canonical_sha256":"3d502ae9387be54ddde9bc2502b142d6cc7c78e0f9b34e47b1badde3ae3ac007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d502ae9387be54ddde9bc2502b142d6cc7c78e0f9b34e47b1badde3ae3ac007","first_computed_at":"2026-05-18T00:24:40.006528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:40.006528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ogZxXORoTheXyk04gWsS5ppVdGNmfw7El/WD3engZy1cou4sxuhA4u2XXOZ5/MiBVga3zd0z/lyVG1V0Mt+gCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:40.007085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02884","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01a7894c7b5739d3ce8057b6e2f196e90b028ffeab67a9ecf155f5d1dba02fa0","sha256:802f98693c9a8ae81c6290dd9058c2f44f5aafb9cd3cfd6a3c415cd8b00b3e10"],"state_sha256":"45212a81f77927d66e206ff82715df95e435d07aed5e5c8c561d03870616023a"}